In this paper, we present and analyze two block-centered local refinement (BLR) methods for solving the time-fractional equations. The main difference between the two methods is that different ...approximation methods are used for the value of the pressure at the slave nodes. One adopts a piecewise constant interpolation approximation (PCIA) method, which is called simple block-centered local refinement (S-BLR) method. The other utilizes a piecewise linear interpolation approximation (PLIA) method, which called more accurate block-centered local refinement (MA-BLR) method. The stability analysis is proved carefully. It is estimated that the discrete L2 errors for the velocity and pressure are O(▵t2−α+h3/2) and O(▵t2−α+h3/2) in use of S-BLR and MA-BLR methods, respectively. Where Δt is the time step and h is the maximal mesh size. These error estimate results are all established on locally refinement composite grids. Finally, a numerical experiment is presented to show that the convergence rates are in agreement with the theoretical analysis.
This paper provides an Isogeometric Indirect Boundary Element Method (IGIBEM) based on NURBS (Non-Uniform Rational B-Splines) and PHT-splines (polynomial splines over hierarchical T-meshes) for ...analyzing the three-dimensional (3D) acoustic problems. In the classical procedure, the geometries are discretized by Lagrange polynomials elements, which leads to both substantial geometrical error and time-consuming meshing steps. However, these deficiencies can be eliminated by the isogeometric analysis (IGA) directly incorporating the geometry description generated from the CAD (Computer Aided Design) software into CAE (Computer Aided Engineering) analysis. Unlike the DBEM (direct boundary element method), the IBEM (indirect boundary element method) allows different types of boundary conditions on the two sides of a surface. Moreover, the hypersingular integrals in IBEM can be transformed to a weakly singular form. In addition, the PHT-based IBEM is used to investigate the influence of local refinement on the accuracy of solutions. Finally, the non-uniqueness problem is solved, which is a fatal defect in the acoustic BEM for the exterior problem. Four different methods to handle the non-uniqueness problem are discussed and compared. The results obtained by the proposed method were compared with analytical solutions and the results computed by Lagrange-based IBEM. Several benchmark examples demonstrate: (1) the present method, i.e. IGIBEM, has super accuracy over conventional IBEM for the acoustic problems; (2) local refinement has a significant influence on the convergence rate of the solutions, and the numerical accuracy is relevant to the distance to the boundary where the local refinement acted; (3) as for the non-uniqueness problem, the imposition of specific interior boundary conditions not only obtains the best calculation result over the entire range of frequencies, but also has a simple integral formulation.
•We implement an IGIBEM based on NURBS and PHT-splines for 3D acoustic problems.•The NURBS-based IBEM has super accuracy over the Lagrange-based IBEM.•The PHT-based IBEM was proposed to investigate the effect of local refinement on solution domain.•We investigated four indirect boundary integral equations to overcome the non-uniqueness problem.•The imposition of specific interior boundary conditions has simple integral formulation and the best calculation result.
•We present a memetic feature selection algorithm for multi-label classification.•This method employs memetic procedures to refine the feature subsets found through GAs.•This hybridization improves ...the multi-label classification performance compared to counterparts.
The use of multi-label classification, i.e., assigning unseen patterns to multiple categories, has emerged in modern applications. A genetic-algorithm based multi-label feature selection method has been considered useful because it successfully improves the accuracy of multi-label classification. However, genetic algorithms are limited to identify fine-tuned feature subsets that are close to the global optimum, which results in a long runtime. In this paper, we present a memetic feature selection algorithm for multi-label classification that prevents premature convergence and improves the efficiency. The proposed method employs memetic procedures to refine the feature subsets found through a genetic search, resulting in an improvement in multi-label classification. Empirical studies using various tests show that the proposed method outperforms conventional multi-label feature selection methods.
In this article we introduce all the ingredients to develop adaptive isogeometric methods based on hierarchical B-splines. In particular, we give precise definitions of local refinement and ...coarsening that, unlike previously existing methods, can be understood as the inverse of each other. We also define simple and intuitive data structures for the implementation of hierarchical B-splines, and algorithms for refinement and coarsening that take advantage of local information. We complete the paper with some simple numerical tests to show the performance of the data structures and algorithms, that have been implemented in the open-source Octave/Matlab code GeoPDEs.
Local refinement with hierarchical B-spline structures is an active topic of research in the context of geometric modeling and isogeometric analysis. By exploiting a multilevel control structure, we ...show that truncated hierarchical B-spline (THB-spline) representations support interactive modeling tools, while simultaneously providing effective approximation schemes for the manipulation of complex data sets and the solution of partial differential equations via isogeometric analysis. A selection of illustrative 2D and 3D numerical examples demonstrates the potential of the hierarchical framework.
In this paper we present a new method termed Truncated Hierarchical Catmull–Clark Subdivision (THCCS), which generalizes truncated hierarchical B-splines to control grids of arbitrary topology. THCCS ...basis functions satisfy partition of unity, are linearly independent, and are locally refinable. THCCS also preserves geometry during adaptive h-refinement and thus inherits the surface continuity of Catmull–Clark subdivision, namely C2-continuous everywhere except at the local region surrounding extraordinary nodes, where the surface continuity is C1. Adaptive isogeometric analysis is performed with THCCS basis functions on a benchmark problem with extraordinary nodes. Local refinement on complex surfaces is also studied to show potential wide application of the proposed method.
•Modeling holes in orthotropic media by an effective adaptive XIGA based on LR B-splines is presented.•The location of hole interfaces is represented by multiple level set functions, distinguishing ...different types of elements.•A stress recovery technique for XIGA is developed.•Local refinement is conducted through the posteriori error estimation using structured meshes.•Complex geometries of holes can be conveniently modeled by the present approach.
We present in this paper an efficient computational approach based on an adaptive extended isogeometric analysis (XIGA) for simulation of arbitrary holes in orthotropic materials. The interfaces of holes are described by multiple level set functions so that the developed XIGA can capture the hole geometry without considering its interfaces. The approach is further enhanced by using the locally refined (LR) B-spline basis functions, which dominate over B-spline or non-uniform rational B-spline functions (NURBS) due to the local refinement. This study only deals with the structured mesh strategy for local refinement. The implementation of the local refinement is guided by posteriori error estimator based on stress recovery. Accuracy study is performed for isotropic media due to the availability of analytical solutions. For numerical experiments, different types of holes in orthotropic media are studied, and the computed numerical results are compared with reference solutions derived from ABAQUS (FEM). We also compare the convergence rate obtained by our adaptive local refinement with that derived from uniform global refinement to indicate the greater advantage of the developed adaptive XIGA.
We develop a local refinement algorithm for analysis-suitable T-splines which does not produce excessive propagation of control points. We then demonstrate its use as an adaptive framework for ...isogeometric analysis. Analysis-suitable T-splines are a class of T-splines which are linearly independent and form a partition of unity. These properties, coupled with local refinement, make this class of T-splines appealing as a basis for isogeometric analysis.
Fracture analysis of orthotropic cracked media is investigated by applying the recently developed extended isogeometric analysis (XIGA) (Ghorashi et al., 2012) using the T-spline basis functions. The ...signed distance function and orthotropic crack tip enrichment functions are adopted for extrinsically enriching the conventional isogeometric analysis approximation for representation of strong discontinuity and reproducing the stress singular field around a crack tip, respectively. Moreover, by applying the T-spline basis functions, XIGA is further developed to make the local refinement feasible. For increasing the integration accuracy, the ’sub-triangle’ and ’almost polar’ techniques are adopted for the cut and crack tip elements, respectively. The interaction integral technique developed by Kim and Paulino (2003) is applied for computing the mixed mode stress intensity factors (SIFs). Finally, the proposed approach is applied for analysis of some cracked orthotropic problems and the mixed mode SIFs are compared with those of other methods available in the literature.
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